Quantum computing utilizes quantum particles to carry out computational processes. The fundamental unit of quantum information is called a quantum bit or qubit. A qubit can be both a zero and a one at the same time. An example is the spin of an electron, wherein the up or down spin can correspond to a zero, a one, or a superposition of states in which it is both up and down at the same time. Performing a calculation using the electron essentially performs the operation simultaneously for both a zero and a one. Experimental advances in quantum computation have come most rapidly in nuclear magnetic resonance (NMR) and ion-trap systems. The success of few-qubit quantum computation in such systems demonstrates an urgent need for a quantum computing scheme that is scaleable to a large number of qubits. Solid-state qubits are one of the primary candidates. Numerous proposals have been made for solid-state quantum computers. These proposals include the use of nuclear spins as qubits, B. E. Kane, “A Silicon-Based Nuclear Spin Quantum Computer,” Nature, Vol. 393 (6681), (1998), pp. 133-137; and the use of electronic spins as quantum dots, DiVincenzo, et al., “Quantum Computers and Quantum Coherence,” J. of Magnetism and Magnetic Materials, Vol. 200, (1-3), 1999, pp. 202-218. Potential issues with such proposed systems include individual impurity spins, as well as gate operation and readout methods for the quantum dots.
Spins can be manipulated using a strong DC magnetic field combined with a radio frequency field (e.g., at GHz frequencies). In the presence of a small g-factor gradient, the spins can be addressed individually. Entanglement of one spin with another proceeds by gating the barrier between spins. This gives rise to a time-dependent exchange interaction, H(t)=J(t)S1S2. A combination of these operations acting in the proper sequence on two qubits will produce a controlled-NOT gate (C-NOT). See, e.g., R. Vrijen, et al., “Electron-Spin Resonance Transistors for Quantum Computing in Silicon-Germanium Heterostructures,” Physical Review A, Atomic, Molecular, and Optical Physics, Vol. 62(1), 2000, pp. 012306/1-10.
Quantum dot architectures have been developed specifically for the purpose of manipulating electron spins for fast and accurate two-qubit operations that serve as universal gates for quantum computations. M. Friesen, et al., Phys. Rev. B 67, 121301-1-4 (2003). See, also, U.S. Pat. No. 6,597,010. Recent experimental results have shown that decoherence does not pose a fundamental problem for such gate operations. A. M. Tyryshkin, et al., Phys. Rev. B 68, 193207 (2003). Using special qubit geometries as discussed in M. Friesen, et al., Appl. Phys. Lett. 81, 4619 (2002), it should be possible to perform reliable gate operations in silicon quantum dots at rates between about 1 MHz and 1 GHz.
In a quantum computer, qubits are usually stored in physical devices that are localized, and qubit gating often involves local interactions. For example, the gating of spin-based qubits conventionally involves only nearest neighbors. D. Loss, et al., “Quantum Computation with Quantum Dots,” Phys. Rev. A 57, 120-126 (1998). Conceptually, it is possible to implement quantum gates between any pair of distant qubits by using enough intermediate SWAP gates to bring the qubits into proximity. See, M. A. Nielson and L. I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000. While such procedures would not affect the exponential nature of algorithmic speedup for prime factorization, they could be detrimental for algorithms with sub-exponential speedup. In particular, because of the nested structure of fault-tolerant algorithms, the absence of long-range couplings could be catastrophic, effectively putting error correction out of reach.
In several proposed quantum computing architectures, the problem of short-range interactions is overcome by means of a so called bus mode—a quantum coherent mode extending across the entire device. In principle, different qubits can be coupled to one another via the bus mode. Because of the extended nature of the bus, the proximity of the interacting qubits becomes irrelevant. The bus mode circumvents the need for multiple, local SWAP operations, thus improving the prospects for scalability and fault-tolerance. However, because of the physical extent of the bus, these modes have a tendency to couple more strongly to the environment than localized qubits, with a consequent effect on bus decoherence. Additionally, it often is the case that bus modes couple rather weakly to the qubits, causing a decrease in the bus speed. Quantum computing architectures based on bus modes have been proposed for various physical systems, including trapped ions, where the bus is formed by the phonon modes of a linear array of coupled ions, and solid-state implementations including discrete LC circuits, large Josephson junctions, three-dimensional cavities, grain-boundary phase qubits, and one-dimensional transmission line resonators. Another solid-state quantum computing implementation which has received considerable attention utilizes quantum dots containing a small, fixed number of electrons. Because of the technological infrastructure built around semiconductors, and the attractive decoherence properties of spins in quantum dots, such systems hold promise of highly scalable quantum computing. D. Loss, et al., (1998) supra. However, viable bus architectures for such quantum dot solid-state systems have been difficult to achieve because of the lack of viable bus schemes that are technologically compatible with semiconductor heterostructures. Imamoglu, et al., “Quantum Information Processing Using Quantum Dot Spins and Cavity QED,” Phys. Rev. Lett., 83, 4204-4207 (1999), developed a bus scheme in which spins in self-assembled dots are made to interact in a high-Q cavity by means of laser excited Raman transitions. Unfortunately, the physical realization of this scheme has apparently not been achieved, in part because this approach requires precisely positioned lasers that are extremely difficult to realize experimentally. More recently, it has been proposed to couple spin qubits via a high-Q superconducting transmission line. L. Childress, et al., “Mesoscopic Cavity Quantum Electrodynamics with Quantum Dots,” Phys. Rev. A, vol. 69, pp. 042302-1-8 (2004). Using far off-resonant microwave Raman transitions, the spins can be excited into virtual charge states that interact via the bus. The decoherence problems that normally plague charge-based qubits are reduced in this scheme, due to the detuning of the Raman transitions. However, detuning also considerably reduces the speed of information transfer. Consequently, long-range coupling remains among the chief architectural challenges for scalable spin-based quantum computing.